Tu T. C. Nguyen | Searcharxiv

arXiv2021

Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals

This paper presents a classification of 7-dimensional real and complex indecomposable solvable Lie algebras having some 5-dimensional nilradicals. Afterwards, we combine our results with those of Rubin and Winternitz (1993), Ndogmo and Winternitz (1994), Snobl and Winternitz (2005, 2009), Snobl and Karásek (2010) to obtain a complete classification of 7-dimensional real and complex indecomposable solvable Lie algebras with 5-dimensional nilradicals. In association with Gong (1998), Parry (2007), Hindeleh and Thompson (2008), we achieve a classification of 7-dimensional real and complex indecomposable solvable Lie algebras.

math.RA↗

arXiv2018

On the classifying problem for the class of real solvable Lie algebras having 2-dimensional or 2-codimensional derived ideal

Let $\mathrm{Lie} \left(n, k\right)$ denote the class of all $n$-dimensional real solvable Lie algebras having $k$-dimensional derived ideal ($1 \leqslant k \leqslant n-1$). In 1993, the class $\mathrm{Lie} \left(n, 1\right)$ was completely classified by Schöbel \cite{Sch93}. In 2016, Vu A. Le et al. \cite{VHTHT16} considered the class $\mathrm{Lie} \left(n, n-1\right)$ and classified its subclass containing all the algebras having 1-codimensional commutative derived ideal. One subclass in {\Li} was firstly considered and incompletely classified by Schöbel \cite{Sch93} in 1993. Later, Janisse also gave an incomplete classification of {\Li} and published as a scientific report \cite{Jan10} in 2010. In this paper, we set up a new approach to study the classifying problem of classes {\Li} as well as {\li} and present the new complete classification of {\Li} in the combination with the well-known Eberlein's result of 2-step nilpotent Lie algebras from \cite[p.\,37--72]{Ebe03}. The paper will also classify a subclass of {\li} and will point out missings in Schöbel \cite{Sch93}, Janisse \cite{Jan10}, Mubarakzyanov \cite{Mub63a} as well as revise an error of Morozov \cite{Mor58}.

math.RA↗